The present invention relates in general to processes for forming webs of sheet material and, more particularly, to methods for quickly determining accurate models to characterize the two-dimensional responses of cross-machine direction (CD) actuators used to control the operation of such web forming machines.
Many sheet-forming processes such as paper machines, plastic film extruders, super-calenders, coaters, and similar processes face common process control problems in producing webs which satisfy specifications for the given sheet material. Web specifications commonly include ranges for characteristics of the web including thickness, moisture content, weight per unit area and the like. Quality control is complicated since the specified characteristics vary in both the machine direction (MD) or direction of movement of the web through the machine and also in the cross-machine direction (CD) or laterally across the web.
The MD variations are generally affected by factors that impact the entire width of the web, such as machine speed, the source of base material being formed into a web by the machine, common supplies of working fluids like steam, and similar factors. CD variations, represented by profiles or profile signals, are normally controlled by arrays of actuators distributed across the width of the machine. On paper making machines, for which the present invention is particularly applicable, the CD actuators include basis weight actuators which control the slice of a headbox and/or headbox dilution valves, steam shower nozzles, infrared heaters which control CD moisture variations, thermal actuators which affect sheet thickness, and other known devices. CD actuators present an extensive control problem since sheet-forming machines can easily have several hundred CD actuators spread across the entire machine width to reduce sheet variability.
Adjustment of CD actuators generally affects a portion of the profile which is wider than the area occupied by the individual actuator. Thus, for controlling the CD profile of a web forming machine, it is important to know which portion of the profile is affected by each CD actuator. The functional relationship that describes which part of the profile is affected by each CD actuator is called "mapping" of the CD actuators. The functional curve that indicates how the process profile is changed by the adjustment of a CD actuator is called the "response shape" of the CD actuators. The mapping and response shape of the CD actuators are referred to herein as the CD responses of the actuators. The machine direction response to CD actuator changes is called the MD dynamics. The combination of the MD dynamics and the CD responses is referred to as the two-dimensional (2D) responses of the CD actuators.
Not only does the CD response of each actuator typically spread over a much wider area than the area occupied by the actuator, but also the CD mapping of an actuator can vary or shift for different operating conditions. To obtain a desired profile for a web of sheet material being formed, it is essential to have two-dimensional (2D) information which closely corresponds to each actuator and also to the different operating conditions which the actuator encounters. Thus, the performance of a CD control application is highly dependent on the accuracy of the models that characterize the responses of all CD actuators. In practice, the actuator response models have to be identified from the sheet-forming machines by performing actuator tests. Using an effective method to identify robust response models is very crucial to achieve the optimal control results for any CD control application.
The profile response as the result of a control action applied to a CD actuator is usually obtained through a so-called "bump" test or a "step" setpoint change to a CD actuator. The responses from adjacent CD actuators usually overlap with one another in the CD direction so that conventional CD bump-tests can only be applied to actuators that are far enough apart to have no overlapping effects in order to separate their responses. This problem is exacerbated where a scanning sensor is used to measure the profile responses. The scanning sensor only measures sheet property profiles along diagonal traces across the sheet width. With the extremely sparse and skew data obtained from a scanning sensor, a bump-test usually takes a long time covering multiple scans of the sensor to establish a reliable response model for any CD actuator across the sheet width. The step bump-test itself also suspends the normal control operation and can cause severe product deviations for long duration tests. To get response models for all actuators, it can take many hours to perform many step bump tests so that it is practically infeasible for any production.
An improvement over conventional bump testing is disclosed in U.S. Pat. No. 5,122,963, which issued to the assignee of the present application and is incorporated herein by reference. In the '963 patent, CD actuator perturbing signals defined by pseudo-random binary sequences are used with multiple signals being selected to be statistically independent of one another so that the responses of multiple CD actuators can be determined at the same time. The perturbing signals are gradually increased in amplitude to a level which can be used for CD analysis yet not perturb the web beyond defined specifications. While the teachings of the '963 patent substantially speed up the determination of CD actuator models over conventional bump tests, they still require a substantial period of time since numerous scans of a scanning sensor are still required to characterize all CD actuators.
Since for many sheet-making processes, the two-dimensional, i.e., machine direction and cross-machine direction, uniformity of sheet properties is a critical quality specification, new methods for getting accurate response models for each CD actuator in a sheet-making process are needed to achieve better sheet uniformity control. Preferably, the testing period and product deviations caused by the tests would be reduced for tuning any CD control application. In addition, the new methods should not only reduce the required testing duration and product deviations, they should also identify the two-dimensional (2D) response of each CD actuator individually.